Model Proceeding E Book 4A Turky

991 In the next period, the fir m‘s stock price is determined in the market. The market model we use is an extension of Kyle 1985. Here, the stock market comprises a single risk-neutral informed trader, uninformed traders and a competitive risk-neutral market maker. The manager releases public information concerning the future returns of the investment and trading takes place. The informed trader observes the public earnings information and privately observes another signal, and then submits orders x fo r the firm‘s stock given this information. Uninformed traders can observe none of this kind of information and can submit random orders of u u  ~ where . That is, the informed trader‘s trading is exogenous. The market maker observes the public information and additionally observes total orders of u x Y   . The market maker sets price such that he expects to earn a zero profit given the total orders and public earnings information. The presence of uninformed traders makes it impossible for the market maker to infer exactly the informed trader‘s private information. Private information , which only the informed trader will receive, is normally distributed with zero mean and unit variance; that is, . The public earnings information , which can be observed by both the informed trader and the market maker, is also normally distributed with zero mean and unit variance; that is, . The random investment return and signals and are correlated, and are denoted by , and , respectively. Without loss of generality, we assume that . That is, signals and are positively correlated with investment return otherwise, the opposing signal can be used instead of the original signal; therefore, these signals are also positively correlated with each other. 992 In equilibrium, the manager chooses the investment level by anticipating the effects of her decision on the firm‘s stock price . The price is determined in the market such that the informed trader‘s anticipation of the price and the actual price are equal. The following provides a definition of the equilibrium of this model. Definition We define equilibrium in this model as a pair such that the following three conditions hold: 1. The manager invests to maximize her expected utility, . 2. The informed trader makes orders x subject to for any alternative trading strategy x‘ and for any v, . 3. The price is determined such that the market maker receives zero expected profits, .

3. Equilibrium analysis

3.1 Equilibrium in the model

We focus on the optimal investment decision by the manager. The manager makes her investment decision by anticipating the effects of her investment decision on the stock price of the firm. The market maker, observing both the total order flow x u Y   and the public earnings information e provided by the manager, then sets the stock price. Using backward induction, we first find the equilibrium stock price P and the optimal order amount x , cond itional on the manager‘s investment. In 993 deriving the equilibrium in this model, we focus on the linear equilibrium. It is well known that this equilibrium concept is the same as Kyle 1985. We then solve for the optimal investment decision by the manager. The following lemma provides the characterization of the equilibrium stock price and the demand of informed traders. Lemma 1. The unique equilibrium is given by: e s x 2 1     , and   e x u v e Y v P 2 1 2 1              , where 2 1 1 se u      , 2 2 1 se se u      － ,   2 1 2 1 se u se Ve Vs           and Ve    2 . Proof. See Appendix A. We see that the informed trader places different weights on the private and public earnings information in making a decision on his demand. Further, we also see that these two weights are in the opposite direction. The relative weight is se    －  2 1 . Therefore, the informed trader is attaching relatively greater importance to his private signal than the public earnings signal as the correlation between the two signals becomes higher.